Acoustic Radiation Force (ARF) shear wave elasticity imaging methods typically use a transverse propagation velocity of mechanical shear waves in materials to estimate mechanical properties of a sample, such as material elasticity constants. These techniques may be adapted into imaging systems to compute the local shear wave propagation velocity as a function of both axial and lateral position. The velocity may be calculated by estimating the differences in arrival times of the shear waves, either at different recording locations or from different excitation locations.
The velocity of the shear wave may, therefore, be estimated over a predefined lateral kernel or distance. The shear wave velocity is typically estimated using a time-of-flight based reconstruction technique that assumes a known direction of wave propagation and a homogeneous, isotropic tissue within the reconstruction kernel. Violations of these assumptions, however, can lead to biased shear wave speed estimates and image artifacts generated by reflected waves at the structural boundaries.
For example, acoustic radiation force (ARF) arises from a transfer of momentum from a sound wave to the medium through which it is traveling due to both absorption and scattering of the wave and is described by K. R. Nightingale, M. Palmeri, R. Nightingale, and G. Trahey, “On the feasibility of remote palpation using acoustic radiation force,” J Acoust Soc Am, vol. 110, pp. 625-634, 2001 and G. R. Torr, “The Acoustic Radiation Force,” Am. J. Phys., vol. 52, pp. 402-408, 1984.
                              F          →                =                              2            ⁢            α            ⁢                                                  ⁢                          I              →                                c                                    (        1        )            where α is the acoustic attenuation, I is the acoustic intensity, c is the speed of sound, and F is the force applied to the medium. SWEI utilizes this acoustic radiation force by applying ultrasonic pushing pulses that displace the tissue on the order of microns and tracking the propagation of the transverse wave that propagates away from the region of excitation.
A typical ARF-induced shear wave beam sequence begins with acquiring at least one conventional reference A-line in the region of interest (ROI), then applying the pushing pulse away from the ROI, and finally acquiring additional tracking A-lines. The response of the tissue is determined by estimating the displacement of the tissue between the pre-push reference and the post-push tracks. By observing how the shear wave propagates over multiple tracking lateral locations or multiple pushing lateral locations, it is possible to estimate the shear wave speed (SWS). Under the assumptions of homogeneous, linear elastic, incompressible, isotropic tissue, the shear modulus (G) is equal to three times the Young's modulus (E), and also equal to the density of the tissue (ρ) times the shear wave speed (S) squared (i.e., G=3E=ρg2). Thus, stiffer tissues have a higher shear wave speed than soft tissues, and by creating images of the shear wave speed, or derived shear or Young's modulus, the image contrast is related to the stiffness of the underlying tissue.
To estimate the SWS, the wave arrival time at each lateral and axial location is determined. Multiple methods exist for determining this wave arrival time, such as time-to-peak tissue displacement, time-to-peak tissue velocity, and cross-correlation between the displacement or velocity profiles at each lateral location. Typically, these wave arrival time estimates are then input into a time-of-flight algorithm, such as linear regression or random sample consensus, which fits the data to a model assuming a single shear wave speed across the lateral and axial reconstruction kernel. Specifically, linear regression is a maximum likelihood estimator that assumes a linear relationship between the arrival time at each location and the speed of the shear wave. In structured media, to obtain high resolution, small regression kernels are desired, but this leads to increased noise in the estimated SWS.